Contemporary English Version (CEV)
It feels good to be right, especially when you are affirmed publicly. It's even better when you being right means that someone else is wrong, isn't it? You look even better in contrast. We spend a lot of time doing this -- looking for someone else to be wrong so that we can look even better. If you have paid even a moment of attention to politics, you know this is how it works -- it's not just about winning, but it's as much about making your opponent lose.
The Pharisees really enjoyed pointing out the sins of others. They would run around and try to find other people who were busy sinning, because in doing so, they could look even better, even more righteous. While they couldn't achieve perfection, they could look darn close by making everyone else look downright rotten.
Jesus, however, isn't really interested in our efforts to prop ourselves up by the sins of others. Jesus is interested in our hearts, and our own relationship with God, which should affect our relationship with others (it should be challenging to hold malice towards others when we have been forgiven of so much). Jesus wants us to recognize our own brokenness and cast ourselves on the grace of Christ, worrying not about the sins of others but instead just focused on the grace and love of Christ.
Notice, too, the charge Jesus gives her. She is free from her sins, but she is charged with a responsibility -- to go and sin no more. This is certainly impossible, but our transformation in Christ is not a one time thing. It affects the rest of our lives, and we, too, are sent forth on a mission.